John Forbes Nash Jr. (June 13, 1928 – May 23, 2015), professionally recognized as John Nash, was a distinguished American mathematician whose seminal work significantly advanced game theory, real algebraic geometry, differential geometry, and partial differential equations. Alongside fellow game theorists John Harsanyi and Reinhard Selten, Nash received the 1994 Nobel Memorial Prize in Economic Sciences. In 2015, he and Louis Nirenberg were jointly honored with the Abel Prize for their profound impact on the domain of partial differential equations.
John Forbes Nash Jr. (June 13, 1928 – May 23, 2015), known and published as John Nash, was an American mathematician who made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations. Nash and fellow game theorists John Harsanyi and Reinhard Selten were awarded the 1994 Nobel Prize in Economics. In 2015, Louis Nirenberg and he were awarded the Abel Prize for their contributions to the field of partial differential equations.
During his graduate studies within the Princeton University Department of Mathematics, Nash pioneered several foundational concepts, including the Nash equilibrium and the Nash bargaining solution, which have become cornerstones of game theory and its diverse scientific applications. Throughout the 1950s, Nash formulated and demonstrated the Nash embedding theorems through the resolution of a system of nonlinear partial differential equations originating from Riemannian geometry. This particular research, which also presented an early iteration of the Nash–Moser theorem, was subsequently acknowledged by the American Mathematical Society with the prestigious Leroy P. Steele Prize for Seminal Contribution to Research. Collaborating independently, Ennio De Giorgi and Nash developed a series of findings that established a framework for a comprehensive comprehension of elliptic and parabolic partial differential equations. Their collaborative De Giorgi–Nash theorem, addressing the smoothness of solutions for these equations, successfully resolved Hilbert's nineteenth problem concerning regularity in the calculus of variations, a prominent unresolved issue for nearly six decades.
By 1959, Nash exhibited symptoms of mental illness, leading to several years of hospitalization in psychiatric facilities where he received treatment for schizophrenia. Subsequent to 1970, his health gradually stabilized, enabling his reintegration into academic pursuits by the mid-1980s.
The life of John Nash served as the inspiration for Sylvia Nasar's 1998 biographical work, A Beautiful Mind. His personal challenges with mental illness and subsequent recovery were also dramatized in a film adaptation bearing the same title, directed by Ron Howard, where Russell Crowe depicted Nash.
Early Life and Academic Background
John Forbes Nash Jr. was born on June 13, 1928, in Bluefield, West Virginia. His father, John Forbes Nash Sr., an electrical engineer, shared his name. His mother, Margaret Virginia (née Martin) Nash, had worked as a schoolteacher prior to her marriage. He was baptized into the Episcopal Church and had one younger sister, Martha, born on November 16, 1930.
Nash's early education included kindergarten and public schooling, supplemented by self-study from books provided by his family. His parents actively sought to enhance his academic development, arranging for him to undertake advanced mathematics courses at Bluefield College (now Bluefield University) during his senior year of high school. He subsequently enrolled at the Carnegie Institute of Technology (later Carnegie Mellon University) with the support of a George Westinghouse Scholarship, initially pursuing chemical engineering. He later transitioned to a chemistry major before ultimately specializing in mathematics, a decision influenced by his instructor, John Lighton Synge. Upon earning both Bachelor of Science and Master of Science degrees in mathematics in 1948, Nash accepted a prestigious fellowship to Princeton University, where he continued his postgraduate studies in mathematics and related scientific disciplines.
Richard Duffin, Nash's advisor and former professor at Carnegie Tech, provided a letter of recommendation for his admission to Princeton, asserting, "He is a mathematical genius." Nash received acceptance offers from multiple prestigious institutions, including Harvard University, the University of Chicago, and the University of Michigan. Nevertheless, Solomon Lefschetz, the chairman of Princeton's mathematics department, extended the John S. Kennedy fellowship, which persuaded Nash that Princeton held his potential in higher regard. Additionally, Princeton's geographical proximity to his family in Bluefield was a significant factor in his decision. It was at Princeton that he commenced his foundational work on equilibrium theory, subsequently formalized as the Nash equilibrium.
Research Contributions
Despite a relatively modest publication record, many of Nash's scholarly articles are recognized as seminal contributions within their respective disciplines. During his graduate studies at Princeton, he established fundamental concepts in both game theory and real algebraic geometry. Subsequently, as a postdoctoral researcher at MIT, Nash shifted his focus to differential geometry. While his findings in differential geometry are articulated using geometric terminology, the underlying methodology predominantly involves the mathematical analysis of partial differential equations. Following the successful demonstration of his two isometric embedding theorems, Nash transitioned to direct research on partial differential equations, culminating in the discovery and proof of the De Giorgi–Nash theorem, which provided a solution to a specific aspect of Hilbert's nineteenth problem.
In 2011, the National Security Agency released declassified correspondence from the 1950s, revealing Nash's proposal for an innovative encryption–decryption apparatus. This correspondence indicates that Nash foresaw numerous principles of contemporary cryptography, particularly those founded on computational hardness.
Game Theory
In 1950, Nash completed his doctoral degree with a 28-page dissertation focusing on noncooperative games. This thesis, supervised by his doctoral advisor Albert W. Tucker, introduced the definition and fundamental properties of the Nash equilibrium, a pivotal concept within noncooperative game theory. An adapted version of his dissertation appeared in the Annals of Mathematics one year subsequently. Throughout the early 1950s, Nash conducted extensive research into various related concepts within game theory, encompassing the theory of cooperative games. His contributions were recognized in 1994 when he was awarded a share of the Nobel Memorial Prize in Economic Sciences.
Real Algebraic Geometry
While still pursuing his graduate studies in 1949, Nash made a significant discovery within the mathematical domain of real algebraic geometry. He formally presented his theorem in a submitted paper at the 1950 International Congress of Mathematicians, despite not having fully elaborated the intricacies of its proof at that time. The complete formulation of Nash's theorem was achieved by October 1951, coinciding with its submission to the Annals of Mathematics. Prior to Nash's work, it was established in the 1930s that any closed smooth manifold is diffeomorphic to the zero locus of a specific set of smooth functions defined on Euclidean space. Nash's contribution demonstrated that these smooth functions could, in fact, be represented as polynomials. This finding was widely considered remarkable, given that the categories of smooth functions and smooth manifolds are typically perceived as considerably more adaptable than the class of polynomials. The methodology employed in Nash's proof introduced the concepts now designated as Nash function and Nash manifold, which have subsequently become subjects of extensive investigation within real algebraic geometry. Notably, Nash's theorem was famously applied by Michael Artin and Barry Mazur in their research on dynamical systems, integrating Nash's polynomial approximation with Bézout's theorem.
Differential Geometry
While holding a postdoctoral appointment at MIT, Nash actively sought out significant mathematical challenges for investigation. He became aware of the conjecture, through differential geometer Warren Ambrose, positing that every Riemannian manifold is isometric to a submanifold within Euclidean space. Nash's findings, which substantiated this conjecture, are now collectively referred to as the Nash embedding theorems; the second of these theorems was notably described by Mikhael Gromov as "one of the main achievements of mathematics of the 20th century".
Nash's initial embedding theorem was formulated in 1953. He demonstrated that any Riemannian manifold can be isometrically embedded into a Euclidean space via a continuously differentiable mapping. Nash's methodology permits a remarkably small codimension for the embedding, implying that in numerous scenarios, the existence of a highly-differentiable isometric embedding is logically precluded. Building upon Nash's techniques, Nicolaas Kuiper subsequently identified even smaller codimensions, leading to an enhanced result frequently termed the Nash–Kuiper theorem. Consequently, Nash's embeddings are constrained to contexts of low differentiability. This limitation positions Nash's finding somewhat outside the conventional focus within differential geometry, a field where high differentiability holds considerable importance in much of its standard analytical framework.
Nevertheless, Nash's methodological framework has proven valuable across numerous other domains within mathematical analysis. Building upon the foundational contributions of Camillo De Lellis and László Székelyhidi, Nash's proof concepts were subsequently employed in the construction of various turbulent solutions for the Euler equations within fluid mechanics. During the 1970s, Mikhael Gromov expanded upon Nash's principles, formulating the comprehensive framework of convex integration. This framework has been utilized, notably by Stefan Müller and Vladimír Šverák, to generate counterexamples for generalized iterations of Hilbert's nineteenth problem in the calculus of variations.
Nash encountered considerable unforeseen challenges in constructing smoothly differentiable isometric embeddings. Nevertheless, following approximately eighteen months of dedicated research, his endeavors culminated in success, establishing the second Nash embedding theorem. The conceptual underpinnings of this second theorem diverge significantly from those employed in the proof of the first. A core component of the proof involves an implicit function theorem specifically tailored for isometric embeddings. Standard formulations of the implicit function theorem proved unsuitable due to technical complexities associated with loss of regularity phenomena. Nash's innovative solution to this problem, which involved deforming an isometric embedding via an ordinary differential equation that continuously introduces additional regularity, is recognized as a groundbreaking technique in mathematical analysis. In 1999, Nash's seminal paper received the Leroy P. Steele Prize for Seminal Contribution to Research. The citation specifically highlighted his "most original idea" in addressing the loss of regularity problem as "one of the great achievements in mathematical analysis in this century". Gromov stated:
One must either be a novice in analysis or a genius comparable to Nash to conceive of such a proposition as true, or to envision even a single non-trivial application.
Following Jürgen Moser's expansion of Nash's concepts to address diverse problems, particularly in celestial mechanics, the resultant implicit function theorem is now designated as the Nash–Moser theorem. Numerous other scholars, including Gromov, Richard Hamilton, Lars Hörmander, Jacob Schwartz, and Eduard Zehnder, have subsequently extended and generalized this theorem. Nash himself investigated the problem within the domain of analytic functions. Schwartz subsequently remarked that Nash's concepts were "not just novel, but very mysterious," and that comprehending them thoroughly proved exceptionally challenging. Gromov further observed:
Nash addressed classical, yet profoundly challenging, mathematical problems that others could neither resolve nor even conceptualize how to approach. Furthermore, the discoveries Nash made during his construction of isometric embeddings transcend 'classical' boundaries, fundamentally reshaping our comprehension of the core principles of analysis and differential geometry. From a classical viewpoint, Nash's accomplishments in his publications appear as improbable as his own life narrative. His contributions to isometric immersions have unveiled a novel mathematical realm, extending into uncharted territories that remain to be fully investigated.
Partial Differential Equations
During his tenure at the Courant Institute in New York City, Nash was apprised by Louis Nirenberg of a prominent conjecture within the domain of elliptic partial differential equations. Although Charles Morrey had established a fundamental elliptic regularity result for functions of two independent variables in 1938, comparable findings for functions involving more than two variables had remained unattainable. Following comprehensive discussions with Nirenberg and Lars Hörmander, Nash successfully extended Morrey's findings, encompassing not only functions of more than two variables but also the framework of parabolic partial differential equations. His research, mirroring Morrey's approach, achieved uniform control over the continuity of solutions for these equations, critically without postulating any specific level of differentiability for the equation's coefficients. The Nash inequality, a specific outcome of his research (the proof of which Nash credited to Elias Stein), has subsequently demonstrated utility in various other mathematical contexts.
Subsequently, Nash was informed by Paul Garabedian, who had recently returned from Italy, that Ennio De Giorgi, then an unknown mathematician, had independently achieved nearly identical results concerning elliptic partial differential equations. Although their methodologies were largely distinct, Nash's approach demonstrated greater versatility, being applicable to both elliptic and parabolic equations. Several years later, Jürgen Moser, drawing inspiration from De Giorgi's method, developed an alternative strategy to arrive at the same conclusions. This collective body of work is now recognized as the De Giorgi–Nash theorem or the De Giorgi–Nash–Moser theory, which is distinct from the Nash–Moser theorem. De Giorgi and Moser's techniques proved particularly instrumental in subsequent years, evolving through the contributions of Olga Ladyzhenskaya, James Serrin, and Neil Trudinger, among others. Their work, primarily founded on the judicious selection of test functions within the weak formulation of partial differential equations, presented a stark contrast to Nash's methodology, which relied on the analysis of the heat kernel. Nash's original contribution to the De Giorgi–Nash theory was later re-examined by Eugene Fabes and Daniel Stroock, leading to a re-derivation and expansion of the results initially derived from De Giorgi and Moser's techniques.
Given that minimizers for numerous functionals in the calculus of variations satisfy elliptic partial differential equations, Hilbert's nineteenth problem, which concerned the smoothness of these minimizers and had been conjectured nearly sixty years earlier, became directly solvable through the De Giorgi–Nash theory. Nash's work garnered immediate acclaim, with Peter Lax characterizing it as a "stroke of genius." Nash later posited that had De Giorgi's discovery not occurred concurrently, he might have been awarded the prestigious Fields Medal in 1958. While the complete rationale behind the medal committee's decisions remains undisclosed and was not solely predicated on mathematical merit, archival investigations have revealed that Nash ranked third in the committee's voting for the medal, following Klaus Roth and René Thom, who were the recipients that year.
Mental Illness
Nash's mental illness initially manifested as paranoia, though his wife subsequently characterized his conduct as erratic. He developed a delusion that all individuals wearing red ties belonged to a "crypto-communist party" actively conspiring against him. He dispatched letters to embassies in Washington, D.C., proclaiming his establishment of a government and signing them "John Nash, Emperor of Antarctica," a title he believed he was destined to inherit. These psychological challenges began to impact his professional life, notably during an American Mathematical Society lecture at Columbia University in early 1959. Nash had intended to present a proof of the Riemann hypothesis, but the lecture proved so disjointed that attending colleagues immediately recognized the severity of his condition.
In April 1959, Nash was admitted to McLean Hospital for a period of one month. His diagnosis was schizophrenia, based on symptoms including paranoid and persecutory delusions, hallucinations, and escalating asociality. Subsequently, in 1961, Nash was admitted to the New Jersey State Hospital at Trenton. Over the ensuing nine years, he underwent intermittent hospitalizations in psychiatric facilities, where he received both antipsychotic medications and insulin shock therapy.
While Nash occasionally adhered to prescribed medication regimens, he later documented that such compliance occurred solely under duress. According to Nash, the film A Beautiful Mind erroneously suggested his use of atypical antipsychotics. He attributed this portrayal to the screenwriter's apprehension that the film might inadvertently encourage individuals with mental illness to discontinue their medication.
Following 1970, Nash ceased all medication and was not subjected to further hospitalizations. His recovery progressed gradually, facilitated by the encouragement of his then-former wife, Alicia Lardé. Nash resided at home and frequented the Princeton mathematics department, where his eccentricities were tolerated even during periods of diminished mental health. Lardé attributed his recovery to the maintenance of "a quiet life" coupled with consistent social support.
Nash identified the onset of his "mental disturbances" in early 1959, coinciding with his wife's pregnancy. He characterized this transformation as a shift "from scientific rationality of thinking into the delusional thinking characteristic of persons who are psychiatrically diagnosed as 'schizophrenic' or 'paranoid schizophrenic'". His delusions included perceiving himself as a messenger with a unique purpose, believing in the existence of supporters, adversaries, and covert schemers, and experiencing feelings of persecution while seeking signs of divine revelation. During his psychotic episodes, Nash also referred to himself in the third person as "Johann von Nassau." He posited that his delusional thought patterns were linked to his unhappiness, his desire for recognition, and his distinctive cognitive style, remarking, "I wouldn't have had good scientific ideas if I had thought more normally." He further stated, "If I felt completely pressureless I don't think I would have gone in this pattern."
Nash reported that he began experiencing auditory hallucinations in 1964, subsequently engaging in a deliberate effort to disregard them. He only relinquished his "dream-like delusional hypotheses" following extended periods of involuntary hospitalization in psychiatric facilities, which he termed "enforced rationality." This renunciation temporarily enabled his return to productive mathematical work. However, he experienced a relapse by the late 1960s. Ultimately, he "intellectually rejected" his "delusionally influenced" and "politically oriented" thoughts, deeming them a futile expenditure of effort. In 1995, he acknowledged that nearly three decades of mental illness had prevented him from realizing his full potential.
In 1994, Nash articulated:
I spent times of the order of five to eight months in hospitals in New Jersey, always on an involuntary basis and always attempting a legal argument for release. And it did happen that when I had been long enough hospitalized that I would finally renounce my delusional hypotheses and revert to thinking of myself as a human of more conventional circumstances and return to mathematical research. In these interludes of, as it were, enforced rationality, I did succeed in doing some respectable mathematical research. Thus there came about the research for "Le problème de Cauchy pour les équations différentielles d'un fluide général"; the idea that Prof. Heisuke Hironaka called "the Nash blowing-up transformation"; and those of "Arc Structure of Singularities" and "Analyticity of Solutions of Implicit Function Problems with Analytic Data".
But after my return to the dream-like delusional hypotheses in the later 60s I became a person of delusionally influenced thinking but of relatively moderate behavior and thus tended to avoid hospitalization and the direct attention of psychiatrists.
Thus further time passed. Then gradually I began to intellectually reject some of the delusionally influenced lines of thinking which had been characteristic of my orientation. This began, most recognizably, with the rejection of politically oriented thinking as essentially a hopeless waste of intellectual effort. So at the present time I seem to be thinking rationally again in the style that is characteristic of scientists.
Recognition and Later Career
In 1978, Nash was honored with the John von Neumann Theory Prize for his groundbreaking discovery of non-cooperative equilibria, now universally known as Nash Equilibria. He subsequently received the Leroy P. Steele Prize in 1999.
In 1994, he was awarded the Nobel Memorial Prize in Economic Sciences, sharing it with John Harsanyi and Reinhard Selten, for his seminal work on game theory conducted during his graduate studies at Princeton. By the late 1980s, Nash had initiated communication via email, gradually connecting with active mathematicians who recognized him as the esteemed John Nash and acknowledged the significance of his contemporary contributions. These individuals formed a core group that contacted the Bank of Sweden's Nobel award committee, providing assurances regarding Nash's mental health and his capacity to accept the prestigious award.
Nash's subsequent research endeavors encompassed advanced game theory, including the concept of partial agency, which underscored his consistent preference for independently selecting his research paths and problems, a characteristic evident throughout his early career. Between 1945 and 1996, he authored 23 scientific publications.
Nash proposed hypotheses concerning mental illness, likening the state of unconventional thought or social nonconformity, often termed "insanity," to an economic "strike." He further articulated perspectives within evolutionary psychology regarding the potential adaptive advantages of seemingly atypical behaviors or societal roles.
Nash expressed criticism of Keynesian monetary economic theories that endorsed central bank intervention in monetary policy. He advocated for a concept of "Ideal Money," which would be indexed to an "industrial consumption price index" and thus offer greater stability compared to what he termed "bad money." He observed that his conceptualizations of currency and the role of monetary authority aligned with those of economist Friedrich Hayek.
Nash was awarded several honorary degrees, including a Doctor of Science and Technology from Carnegie Mellon University in 1999, an honorary degree in economics from the University of Naples Federico II in 2003, an honorary doctorate in economics from the University of Antwerp in 2007, and an honorary doctorate of science from the City University of Hong Kong in 2011. He also delivered a keynote address at a game theory conference. Additionally, he received honorary doctorates from the University of Charleston in 2003 and West Virginia University Tech in 2006. His engagements included numerous guest speaking appearances, notably at the Warwick Economics Summit in 2005.
Nash was inducted into the American Philosophical Society in 2006 and designated a fellow of the American Mathematical Society in 2012.
Just days prior to his demise, on May 19, 2015, Nash, alongside Louis Nirenberg, was conferred the 2015 Abel Prize by King Harald V of Norway during a ceremony held in Oslo.
Personal Life
In 1951, Nash commenced his tenure at the Massachusetts Institute of Technology (MIT) as a C. L. E. Moore instructor within the mathematics faculty. Approximately one year subsequently, Nash initiated a relationship with Eleanor Stier, a nurse whom he encountered during a period of hospitalization. Their union resulted in a son, John David Stier; however, Nash terminated the relationship upon learning of Stier's pregnancy. The biographical film, A Beautiful Mind, faced criticism prior to the 2002 Academy Awards for its omission of this particular detail from his life. Reports indicated that his decision to abandon her was influenced by his perception of her social standing as inferior to his own.
In 1954, during his twenties, Nash was apprehended in Santa Monica, California, on charges of indecent exposure during a police sting operation targeting homosexual men. Despite the subsequent dismissal of these charges, he was divested of his top-secret security clearance and dismissed from his consultancy role at the RAND Corporation.
Shortly after the termination of his relationship with Stier, Nash encountered Alicia Lardé Lopez-Harrison, a naturalized U.S. citizen of Salvadoran origin. Lardé, an MIT alumna, held a degree in physics. Their marriage took place in February 1957. Despite Nash's atheistic convictions, the matrimonial ceremony was conducted in an Episcopal church. By 1958, Nash secured a tenured position at MIT, concurrently with the initial manifestation of his mental illness. He subsequently resigned from MIT in the spring of 1959. Their son, John Charles Martin Nash, was born several months thereafter. The child remained unnamed for a year, as Alicia believed Nash should participate in the naming decision. The strain imposed by his illness led to Nash and Lardé's divorce in 1963. Following his ultimate hospital discharge in 1970, Nash resided in Lardé's home as a boarder. This period of stability appeared beneficial, enabling him to consciously mitigate his paranoid delusions. Princeton University granted him permission to audit courses. He persisted in his mathematical endeavors and was eventually reinstated to a teaching capacity. During the 1990s, Lardé and Nash reconciled, remarrying in 2001.
Their son, John Charles Martin Nash, received a diagnosis of schizophrenia during his high school years and did not complete his secondary education. Nevertheless, he subsequently obtained a Ph.D. in mathematics from Rutgers University.
Death
On May 23, 2015, Nash and his wife tragically died in a vehicular accident on the New Jersey Turnpike in Monroe Township, New Jersey. They were en route home after Nash had received the Abel Prize in Norway. The incident occurred when the driver of their taxi, traveling from Newark Airport, lost control and collided with a guardrail. Both passengers, who were not wearing seatbelts, were ejected from the vehicle and succumbed to their injuries. At the time of his passing, Nash was a long-term resident of New Jersey. He was survived by two sons: John Charles Martin Nash, who resided with his parents, and his elder son, John Stier.
Subsequent to his demise, numerous obituaries were published across global scientific and popular media outlets. Beyond its own obituary for Nash, The New York Times also featured an article compiling various quotes from Nash, sourced from media and other published materials. These quotations encapsulated Nash's personal reflections on his life and accomplishments.
Legacy
During the 1970s at Princeton University, Nash acquired the moniker "The Phantom of Fine Hall," referring to Princeton's mathematics center. He was perceived as an enigmatic presence, frequently observed inscribing complex equations on blackboards during nocturnal hours.
Nash is referenced in Rebecca Goldstein's 1983 novel, The Mind-Body Problem, which is set at Princeton.
Sylvia Nasar's biographical work on Nash, titled A Beautiful Mind, was published in 1998. A film adaptation, also named A Beautiful Mind, premiered in 2001. Directed by Ron Howard, it starred Russell Crowe as Nash and Jennifer Connelly as Alicia, ultimately securing four Academy Awards, including Best Picture. Crowe's portrayal of Nash earned him the Golden Globe Award for Best Actor – Motion Picture Drama at the 59th Golden Globe Awards and the BAFTA Award for Best Actor at the 55th British Academy Film Awards. He also received a nomination for the Academy Award for Best Actor at the 74th Academy Awards.
Awards
- 1978 – Awarded the INFORMS John von Neumann Theory Prize (jointly with Carlton Lemke) in recognition of "their outstanding contributions to the theory of games."
- 1994 – Received the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel (shared with John Harsanyi and Reinhard Selten) "for their pioneering analysis of equilibria in the theory of non-cooperative games."
- 1999 – Conferred the Leroy P. Steele Prize for Seminal Contribution to Research, acknowledging his 1956 paper titled "The imbedding problem for Riemannian manifolds."
- 2002 – Inducted into the class of Fellows of the Institute for Operations Research and the Management Sciences.
- 2010 – Awarded the Double Helix Medal.
- 2015 – Received the Abel Prize (jointly with Louis Nirenberg) "for striking and seminal contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis."
Documentaries and interviews
- Wallace, Mike (host) (March 17, 2002). "John Nash's Beautiful Mind." 60 Minutes. Season 34, Episode 26. CBS.
- Samels, Mark (director) (April 28, 2002). "A Brilliant Madness." American Experience. Public Broadcasting Service. Transcript. Retrieved October 11, 2022.
- Nash, John (September 1–4, 2004). "John F. Nash Jr" (Interview). Interviewed by Marika Griehsel. Nobel Prize Outreach.
- Nash, John (December 5, 2009). "One on One" (Interview). Interviewed by Riz Khan. Al Jazeera English.
- "Interview with Abel Laureate John F. Nash Jr." Newsletter of the European Mathematical Society. Vol. 97. Interviewed by Martin Raussen and Christian Skau. September 2015, pp. 26–31. ISSN 1027-488X. MR 3409221.
Publication list
The following compilation includes four of Nash's game-theoretic papers (Nash 1950a, 1950b, 1951, 1953) and three of his pure mathematics papers (Nash 1952b, 1956, 1958):
- Kuhn, Harold W.; Nasar, Sylvia, eds. (2002). The Essential John Nash. Princeton, NJ: Princeton University Press. doi:10.1515/9781400884087. ISBN 0691095272. MR 1888522. Zbl 1033.01024.
References
Bibliography
- Nasar, Sylvia (1998). A Beautiful Mind. New York: Simon and Schuster. ISBN 978-1439126493.
- Nasar, Sylvia (2002). "Introduction". In Kuhn, Harold W. (ed.), The Essential John Nash. Princeton: Princeton University Press, pp. xi–xxv. ISBN 978-0691096100. JSTOR j.ctt1c3gwz0.
- Siegfried, Tom (2006). A Beautiful Math. Washington, D.C.: Joseph Henry Press. ISBN 978-0309101929.
- O'Connor, John J.; Robertson, Edmund F. "John Forbes Nash Jr." MacTutor History of Mathematics Archive. University of St Andrews.
- Home Page of John F. Nash Jr. at Princeton
- IDEAS/RePEc
- NSA releases Nash Encryption Machine plans Archived February 19, 2012, at the Wayback Machine to National Cryptologic Museum for public viewing, 2012
- Henderson, David R., ed. (2016). "John F. Nash Jr. (1928–2015)." In The Concise Encyclopedia of Economics. Library of Economics and Liberty (2nd ed.). Liberty Fund, pp. 573–74. ISBN 978-0865976665.
- Biography of John Forbes Nash Jr. from the Institute for Operations Research and the Management Sciences
- John Forbes Nash Jr. on Nobelprize.org